Question: Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{7\pi i / 12}) \cdot (3 e^{5\pi i / 12})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{7\pi i / 12}$ ) has angle $\frac{7}{12}\pi$ and radius $2$ The second number ( $3 e^{5\pi i / 12}$ ) has angle $\frac{5}{12}\pi$ and radius $3$ The radius of the result will be $2 \cdot 3$ , which is $6$ The angle of the result is $\frac{7}{12}\pi + \frac{5}{12}\pi = \pi$ The radius of the result is $6$ and the angle of the result is $\pi$.